Determination of Internal Forces for Each Direction and Mode

At the end of any i'th thrust step between two consecutive plastic joint formation, at the end of any displacement, plastic deformation or internal force occurring at any point (j) or section of the conveyor system, the typical magnitude r is represented as _j ⁽ⁱ⁾ and It is calculated by the following equation.

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In the above equation, the value of r _j ⁽ⁱ⁾ is the result of modal combination analysis, in other words, the displacement, plastic deformation or internal force combined with the CQC method. Therefore, first of all, it is necessary to obtain displacement, plastic deformation or internal forces for each direction and each mode. The term is the typical value of displacement, plastic deformation or internal force calculated at any point (j) or section as a result of the linear (linear) mode coupling analysis performed in the i'th step of the repulsion analysis.

For earthquakes in the (X) and (Y) directions, the typical displacement, plastic deformation or internal force increment r _xn ⁽ⁱ⁾ calculated from the point (j) or section of a typical n'th natural vibration mode, in the i'th thrust step of the repulsion analysis, and It is expressed as r _yn ⁽ⁱ⁾ .

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and the terms for earthquakes in (X) and (Y) directions, respectively, belong to a typical n'th natural vibration mode in the i'th step of the thrust analysis, which are taken into account separately. It is the typical value of displacement, plastic deformation or internal force calculated by taking = 1. In the calculation of these terms, the linear (linear) mode combination analysis performed in the i'th step is performed to the system. After finding the real value of the as described in Determination of Modal Pseudo-Acceleration, Modal Displacement Increment and Constant Scale Factor the values ​​of Δr _xn ⁽ⁱ⁾ and Δr _yn ⁽ⁱ⁾ are calculated for each mode with the cumulative scale coefficient.